Parallel Adaptive Interpolation Algorithm based on Sparse Grids for Modeling Dynamic Systems with Interval Parameters

The paper presents a parallel algorithm for adaptive interpolation based on sparse grids for modeling dynamic systems with interval parameters. The idea of the algorithm is to construct a piecewise polynomial function that interpolates the dependence of the solution to the problem on the point values of the interval parameters. In the classical version of the algorithm, polynomial interpolation on complete grids is used, and with a large number of uncertainties, the algorithm becomes difficult to apply due to the exponential growth of computational costs. The use of sparse grids can significantly reduce the computational costs, but nevertheless the complexity of the algorithm in the general case remains exponential with respect to the number of interval parameters. In this regard, the issue of accelerating the algorithm is relevant. The algorithm can be divided into several sets of independent subtasks: updating the values corresponding to the grid nodes; calculation of weighting factors; interpolation of values at new nodes. The last two sets imply parallelization of recursion, so here the techniques for traversing the width of the call graph are mainly used. The parallel implementation of the algorithm was tested on two ODE systems containing two and six interval parameters, respectively, using a different number of computing cores. The results obtained demonstrate the effectiveness of the approaches used.

An optimal method of distribution of the slip zone on thrust bearing surfaces

Research to achieve a reasonable distribution of the slip zone of the sliding pair for better improvement of the hydrodynamic pressure of the liquid film is an intractable topic. To solve this issue, this paper takes the thrust bearing as the research object, and proposes to use the position number of the grid nodes at the boundary line between the slip and no-slip zone in each radial zone of the inclined pad to be variables. The variables are then defined as chromosomes in an adaptive genetic algorithm (AGA) and used to optimize the bearing capacity of the tilting pad. The results show that the optimal method of the AGA, which has good stability and repeatability, remarkably improves the distribution of the slip zone on the surface of the inclined pad. Therefore, the bearing capacity of the liquid film is significantly improved. Particularly, by using the optimization, the boundary line between the slip/no-slip zone is a composite form of a part of an arc and a part of the whisker. When the liquid flow through the heterogeneous slip/on-slip surfaces is used by this composite splicing method, the liquid pressure is upgraded in two steps. This is more conducive to increasing the pressure on multiple areas on the surface of the tilting pad, thereby achieving higher bearing capacity.

Modeling and Analysis of Micro Surface Topography from Ball-End Milling in a Trochoidal Milling Mode

The trochoidal milling mode is widely used in high-speed machining, and due to good adaptability and flexible posture adjustment, ball-end milling cutters are conducive to complex surface machining with this mode. However, the processes of material removal and formation of machined micro surfaces are very difficult to describe as the profile of cutter teeth is complex and the trajectory direction changes continuously during the trochoidal milling process. A modeling method for the generation of micro surface topography of ball-end milling in the trochoidal milling mode is put forward. In this method, the locus equation of each cutter tooth is established based on the principle of homogeneous coordinate transformation, after which a Z-MAP algorithm is designed to simulate the micro surface topography. The Z-MAP algorithm can quickly obtain the part grid nodes potentially swept by the cutter tooth within a unit time step through the establishment of servo rectangular encirclement and instantaneous sweeping quadrilateral of the element of cutter teeth; the part grid nodes actually swept are further determined through an angle summation method, and the height coordinate is calculated with the method of linear interpolation according to Taylor’s formula of multivariate functions. Experiments showed that the micro surface topography resulting from ball-end milling in the trochoidal milling mode had high consistency with the simulation, which indicates that the proposed method can predict micro surface topography in practical manufacturing. In addition, a comparison of micro surface topography between trochoidal milling and ordinary straight-linear milling was conducted, and the results showed that the former was overall superior to the latter in resulting characteristics. Based on this conclusion, the influences of cutting parameters of ball-end trochoidal milling on surface characteristics, particularly amplitude and function, were analyzed according to the simulated micro surface topography data.

Model-to-model data assimilation method for fine resolution ocean modelling

An effective and computationally efficient method is presented for data assimilation in a high-resolution (child) ocean model, which is nested into a coarse-resolution good quality data assimilating (parent) model. The method named Data Assimilation with Stochastic-Deterministic Downscaling (SDDA) reduces bias and root mean square errors (RMSE) of the child model and does not allow the child model to drift away from reality. The basic idea is to assimilate data from the parent model instead of actual observations. In this way, the child model is physically aware of observations via the parent model. The method allows to avoid a complex process of assimilating the same observations which were already assimilated into the parent model. The method consists of two stages: (1) downscaling the parent model output onto the child model grid using Stochastic-Deterministic Downscaling, and (2) applying a simplified Kalman gain formula to each of the fine grid nodes. The method is illustrated in a synthetic case where the true solution is known, and the child model forecast (before data assimilation) is simulated by adding various types of errors. The SDDA method reduces the child model bias to the same level as in the parent model and reduces the RMSE typically by a factor of 2 to 5.

High-Order Data-Driven Spatial Simulation of Categorical Variables

Modern approaches for the spatial simulation of categorical variables are largely based on multi-point statistical methods, where a training image is used to derive complex spatial relationships using relevant patterns. In these approaches, simulated realizations are driven by the training image utilized, while the spatial statistics of the actual sample data are ignored. This paper presents a data-driven, high-order simulation approach based on the approximation of high-order spatial indicator moments. The high-order spatial statistics are expressed as functions of spatial distances that are similar to variogram models for two-point methods, while higher-order statistics are connected with lower-orders via boundary conditions. Using an advanced recursive B-spline approximation algorithm, the high-order statistics are reconstructed from the available data and are subsequently used for the construction of conditional distributions using Bayes’ rule. Random values are subsequently simulated for all unsampled grid nodes. The main advantages of the proposed technique are its ability to (a) simulate without a training image to reproduce the high-order statistics of the data, and (b) adapt the model’s complexity to the information available in the data. The practical intricacies and effectiveness of the proposed approach are demonstrated through applications at two copper deposits.

Large fluctuations in locational marginal prices

This paper investigates large fluctuations of locational marginal prices (LMPs) in wholesale energy markets caused by volatile renewable generation profiles. Specifically, we study events of the form P ( LMP ∉ ∏ i = 1 n [ α i − , α i + ] ) , where LMP is the vector of LMPs at the n power grid nodes, and α − , α + ∈ R n are vectors of price thresholds specifying undesirable price occurrences. By exploiting the structure of the supply–demand matching mechanism in power grids, we look at LMPs as deterministic piecewise affine, possibly discontinuous functions of the stochastic input process, modelling uncontrollable renewable generation. We use techniques from large deviations theory to identify the most likely ways for extreme price spikes to happen, and to rank the nodes of the power grid in terms of their likelihood of experiencing a price spike. Our results are derived in the case of Gaussian fluctuations, and are validated numerically on the IEEE 14-bus test case. This article is part of the theme issue ‘The mathematics of energy systems’.

NUMERICAL ALGORITHM FOR ESTIMATING THE VELOCITY CHARACTERISTICS OF THE MEDIUM IN THE VOLCANIC ZONE

This paper proposes an approach to the calculation and assessment of local velocities of seismic P-waves in a volcanic zone based on the use of the grid method. The numerical algorithm is tested on the experimentally obtained arrival times of P-waves from a vibration source of the SV-10/100 type for the mount Karabetova mud volcano. Registration was carried out by 35 receivers during sounding from 5 points of the vibrator in the frequency range of 10-60 Hz. It follows from the results of numerical modeling that the selection of nonlinearity in the travel time curve of seismic P-waves in the area of a volcanic edifice is possible with the number of grid nodes from 60x60 or more, which corresponds to 31.2 m along the X-axis and 48.1 m along the Y-axis. The obtained results of the distribution of local velocities are consistent with the previously obtained geological structure of the study area and indicate the presence of higher velocities in the area of the anticlinal fold passing through the volcano zone.

Novel Wireless Sensor Network Routing Protocol Performance Evaluation using Diverse Packet Size for Agriculture Application

As the wireless sensor networks (WSNs) progress with newer and more advanced technologies, so do the demands for them in a growing number of applications. Precision agricultural environment monitoring is one of the most prominent applications that require feasible wireless support systems, particularly in the protection and condition control of the crops. This paper focuses on the grid nodes arrangement of WSN, considering the wide dissemination of the plantation areas in the agriculture industry. Due to the different types of sensors used and their data size, the study on the impact of the varied packet size on the performance of the small and large network has been carried out using AODV and OLSR routing protocols. No significant differences in terms of performance can be seen as the packet size is varied. However, compared to the small network, more performance issues have occured in the large network, such as more packet loss, higher throughput degradation, higher energy consumption, worse unfairness, and more overhead production. The OEG routing protocol has been proposed to enhance the network performance by reducing the strain due to the saturated traffic. When solely compared to AODV, OEG routing protocol is able to enhance the network performance with at most 27% more packet delivery ratio, 31kbps more throughput, and 0.991J lesser energy consumed in the network.

Variations of cooling performance on turbine vanes due to incipient particle deposition

In this paper, to demonstrate the deposition effects on cooling performance, the changing patterns of film cooling due to particle deposition are numerically investigated on a turbine vane that is cooled by an array of film-holes. The uniqueness of this work is addressing the cooling performance at an early deposition stage, in which deposits are relatively slight. The build-ups of the deposits are simulated by moving grid nodes on the wall boundaries. Results show that in addition to particle velocity, the blowing conditions and wall temperatures are two important factors to determine the deposition patterns. Increasing coolant-to-mainstream mass flow ratios and lowering wall temperatures can help inhibit the growth of deposits. In addition, the modifications of the vane profile due to incipient deposition are completely different from those with excessive deposition. Although flow fields are less sensitive to the early-stage deposits in the subsonic vane passage, cooling effectiveness is significantly changed and the changes are linked to the mass flow ratios. Compared to the cooling performance from a non-deposition case, reduced cooling performance due to incipient deposition is found at a low mass flow ratio of 1.09%, while cooling performance is improved at moderate and high mass flow ratios of 1.64% and 2.06%.

IZOGRID - A new tool for setting up orthogonal curvilinear grids for oceanic modeling

<p>Virtually all modern structured-grid ocean modeling codes are written in orthogonal curvilinear coordinates in horizontal directions, yet the overwhelming majority of modeling studies are done using very simple grid setups - mostly rectangular patches of Mercator grids rotated to proper orientation.  Furthermore, in communities like ROMS, we even observe decline in both interest and skill of creating curvilinear grids over long term.  This is caused primarily by the dissatisfaction with the existing tools and procedures for grid generation due to inability to achieve acceptable level of orthogonality errors.  Clearly, this causes underutilization of full potential of the modeling codes.</p><p>To address these issues, a new algorithm for constructing orthogonal curvilinear grids on a sphere for a fairly general geometric shape of the modeling region is implemented as a compile-once - use forever software package.  Theoretically one can use Schwartz-Christoffel conformal transform to project a curvilinear contour onto rectangle, then draw a Cartesian grid on it, and, finally, apply the inverse transform (the one which maps the rectangle back to the original contour) to the Cartesian grid in order to obtain the orthogonal curvilinear grid which fits the contour.  However, in the general case, the forward transform is an iterative algorithm of Ives and Zacharias (1989), and it is not easily invertible, nor it is feasible to apply it to a two-dimensional object (grid) as opposite to just one-dimensional (contour) because of very large number of operations.  To circumvent this, the core of the new algorithm is essentially based on the numerical solution of the inverse problem by an iterative procedure - finding such distribution of grid points along the sides of curvilinear contour, that the direct conformal mapping of it onto rectangle turns this distribution into uniform one along each side of the rectangle.  Along its way, this procedure also finds the correct aspect ratio, which makes it possible to automatically chose the numbers of grid points in each direction to yield locally the same grid spacing in both horizontal directions.  The iterative procedure itself turns out to be multilevel - i.e. an iterative loop built around another, internal iterative procedure.  Thereafter, knowing this distribution, the grid nodes inside the region are obtained solving a Dirichlet elliptic problem.  The latter is fairly standard, except that we use "mehrstellenverfahren" discretization, which yields fourth-order accuracy in the case of equal grid spacing in both directions.  The curvilinear contour is generated using splines (cubic or quintic) passing through the user-specified reference points, and, unlike all previous tools designed for the same purpose, it guarantees by the construction to yield the exact 90-degree angles at the corners of the curvilinear perimeter of grid.</p><p>Overall, with the combination of all the new features, it is shown that it is possible to achieve very small, previously unattainable level of orthogonality errors, as well as make it isotropic -- local distances between grid nodes in both directions are equal to each other.</p>